A first-order liquid–liquid phase transition in phosphorus


First-order structural phase transitions are common in crystalline solids, whereas first-order liquid–liquid phase transitions (that is, transitions between two distinct liquid forms with different density and entropy) are exceedingly rare in pure substances1,2,3,4. But recent theoretical and experimental studies have shown evidence for such a transition in several materials, including supercooled water5,6,7,8 and liquid carbon9,10. Here we report an in situ X-ray diffraction observation of a liquid–liquid transition in phosphorus, involving an abrupt, pressure-induced structural change between two distinct liquid forms. In addition to a known form of liquid phosphorus—a molecular liquid comprising tetrahedral P4 molecules—we have found a polymeric form at pressures above 1 GPa. Changing the pressure results in a reversible transformation from the low-pressure molecular form into the high-pressure polymeric form. The transformation is sharp and rapid, occurring within a few minutes over a pressure range of less than 0.02 GPa. During the transformation, the two forms of liquid coexist. These features are strongly suggestive of a first-order liquid–liquid phase transition.

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Figure 1: Experimental paths in a previously reported19,20 phase diagram of black P.
Figure 2: Structure factor, S(Q), for liquid P at several pressures.
Figure 3: Radial distribution function at several pressures derived from S(Q) for liquid P.
Figure 4: X-ray diffraction patterns.


  1. 1

    Young, D. A. Phase Diagram of the Elements (Univ. California Press, 1991).

    Google Scholar 

  2. 2

    Poole, P. H., Grande, T., Angell, C. A. & McMillan, P. F. Polymorphic phase transitions in liquids and glasses. Science 275 , 322–323 (1997).

    CAS  Article  Google Scholar 

  3. 3

    Brazhkin, V. V., Popova, S. V. & Voloshin, R. N. High-pressure transformations in simple melts. High Pressure Res. 15, 267–305 (1997).

    ADS  Article  Google Scholar 

  4. 4

    Ponyatovsky, E. G. & Barkalov, O. I. Pressure-induced amorphous phases. Mater. Sci. Rep. 8, 147 –191 (1992).

    Article  Google Scholar 

  5. 5

    Mishima, O. & Stanley, H. E. The relationship between liquid, supercooled and glassy water. Nature 396, 329–335 (1998).

    ADS  CAS  Article  Google Scholar 

  6. 6

    Poole, P. H., Sciortino, F., Essmann, U. & Stanley, H. E. Phase behaviour of metastable water. Nature 360, 324– 328 (1992).

    ADS  CAS  Article  Google Scholar 

  7. 7

    Harrington, S., Zhang, R., Poole, P. H., Sciortino, F. & Stanley, H. E. Liquid-liquid phase transition: Evidence from simulations. Phys. Rev. Lett. 78, 2409– 2412 (1997).

    ADS  CAS  Article  Google Scholar 

  8. 8

    Mishima, O. & Stanley, H. E. Decompression-induced melting of ice IV and the liquid–liquid transition in water. Nature 392, 164–168 ( 1998).

    ADS  CAS  Article  Google Scholar 

  9. 9

    Togaya, M. Pressure dependence of the melting temperature of graphite and the electrical resistivity of liquid carbon. Phys. Rev. Lett. 79, 2474–2477 (1997).

    ADS  CAS  Article  Google Scholar 

  10. 10

    Glosli, J. N. & Ree, F. H. Liquid-liquid phase transformation in carbon. Phys. Rev. Lett. 82, 4659– 4662 (1999).

    ADS  CAS  Article  Google Scholar 

  11. 11

    Peck, D. R. in Mellor's Comprehensive Treatise on Inorganic and Theoretical Chemistry Vol. VIII, Supp. III, Phosphorus 149–227 (Longman, London, 1971).

    Google Scholar 

  12. 12

    Donohue, J. The Structure of the Elements (Wiley & Sons, New York, 1974).

    Google Scholar 

  13. 13

    Clarke, J. H., Dore, J. C., Granada, J. R., Reed, J. & Walford, G. Neutron diffraction studies of liquid phosphorus I. Reactor and pulsed neutron measurements at 50 °C. Mol. Phys. 42, 861–874 (1981).

    ADS  CAS  Article  Google Scholar 

  14. 14

    Hohl, D. & Jones, R. O. Polymerization in liquid phosphorus: Simulation of a phase transition. Phys. Rev. B 50, 17047–17053 (1994).

    ADS  CAS  Article  Google Scholar 

  15. 15

    Tsuji, K., Yoaita, K., Imai, M., Shimomura, O. & Kikegawa, T. Measurements of X-ray diffraction for liquid metals under high pressure. Rev. Sci. Instrum. 60, 2425–2428 (1989).

    ADS  CAS  Article  Google Scholar 

  16. 16

    Tsuji, K. Structure of liquid metals under high pressure. J. Non-Cryst. Solids 117–118, 27–34 ( 1990).

    ADS  Article  Google Scholar 

  17. 17

    Katayama, Y. et al. Density measurements of liquid under high pressure and high temperature. J. Synchrotron Rad. 5, 1023 –1025 (1998).

    CAS  Article  Google Scholar 

  18. 18

    Katayama, Y., Tsuji, K., Oyanagi, H. & Shimomura, O. Extended X-ray absorption fine structure study on liquid selenium under pressure. J. Non-Cryst. Solids 232–234, 93– 98 (1998).

    Article  Google Scholar 

  19. 19

    Akahama, Y. et al. Melting curve of black phosphorus. Phys. Lett. A 122, 129–131 ( 1987).

    ADS  CAS  Article  Google Scholar 

  20. 20

    Kikegawa, T. et al. Synchrotron-radiation study of phase transitions in phosphorus at high pressures and temperatures. J. Appl. Crystallogr. 20, 406–410 (1987).

    Article  Google Scholar 

  21. 21

    Rapoport, E. Model for melting-curve maxima at high pressure. J. Chem. Phys. 46, 2891–2895 ( 1967).

    ADS  CAS  Article  Google Scholar 

  22. 22

    Misawa, M. Structure factor of X4 tetrahedral molecular liquids: Competition between intramolecular and intermolecular atomic spacings. J. Chem. Phys. 93, 6774–6778 ( 1990).

    ADS  CAS  Article  Google Scholar 

  23. 23

    Elliot, S. R., Dore, J. C. & Marseglia, E. The structure of amorphous phosphorus. J. Phys C 8, 349–353 ( 1985).

    Google Scholar 

  24. 24

    Hohl, D. & Jones, R. O. Amorphous phosphorus: A cluster-network model. Phys. Rev. B 45, 8995– 9005 (1992).

    ADS  CAS  Article  Google Scholar 

  25. 25

    Winter, R. et al. The structural properties of liquid sulphur. J. Phys.: Condens. Matter 2, 8427–8437 (1990).

    ADS  CAS  Google Scholar 

  26. 26

    Aasland, S. & McMillan, P. F. Density-driven liquid–liquid phase separation in the system Al2O3–Y2O 3. Nature 369, 633– 636 (1994).

    ADS  CAS  Article  Google Scholar 

  27. 27

    Mishima, O., Calvert, L. D. & Whalley, E. An apparently first-order transition between two amorphous phases of ice induced by pressure. Nature 314, 76–78 (1985).

    ADS  CAS  Article  Google Scholar 

  28. 28

    Zhao, Y., von Dreele, R. B., Weidner, D. J. & Schiferl, D. P-V-T data of hexagonal boron nitride, hBN, and determination of pressure and temperature using thermoelastic equation of state of multiphases. High Pressure Res. 15, 369– 386 (1997).

    ADS  Article  Google Scholar 

  29. 29

    Endo, S., Akahama, Y., Terada, S. & Narita, S. Growth of large single crystals of black phosphorus under high pressure. Jpn J. Appl. Phys. 21, L482–L484 (1982).

    CAS  Article  Google Scholar 

  30. 30

    Funakoshi, K. & Kawamura, K. A novel intensity correction method for energy-dispersive X-ray diffraction using synchrotron radiation: Application to SiO2 glass at high-pressure. Acta Crystallogr. A (submitted).

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We thank K. Tsuji and Y. Akahama for discussions.

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Correspondence to Yoshinori Katayama.

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Katayama, Y., Mizutani, T., Utsumi, W. et al. A first-order liquid–liquid phase transition in phosphorus. Nature 403, 170–173 (2000). https://doi.org/10.1038/35003143

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